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Where Mathematics Come From : How The Embodied Mind Brings Mathematics Into Being - George Lakoff

Where Mathematics Come From

How The Embodied Mind Brings Mathematics Into Being

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Published: 16th August 2001
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This book is about mathematical ideas, about what mathematics means-and why. Abstract ideas, for the most part, arise via conceptual metaphor-metaphorical ideas projecting from the way we function in the everyday physical world. Where Mathematics Comes From argues that conceptual metaphor plays a central role in mathematical ideas within the cognitive unconscious-from arithmetic and algebra to sets and logic to infinity in all of its forms.

Acknowledgmentsp. ix
Prefacep. xi
Introduction: Why Cognitive Science Matters to Mathematicsp. 1
The Embodiment of Basic Arithmetic
The Brain's Innate Arithmeticp. 15
A Brief Introduction to the Cognitive Science of the Embodied Mindp. 27
Embodied Arithmetic: The Grounding Metaphorsp. 50
Where Do the Laws of Arithmetic Come From?p. 77
Algebra, Logic, and Sets
Essence and Algebrap. 107
Boole's Metaphor: Classes and Symbolic Logicp. 121
Sets and Hypersetsp. 140
The Embodiment of Infinity
The Basic Metaphor of Infinityp. 155
Real Numbers and Limitsp. 181
Transfinite Numbersp. 208
Infinitesimalsp. 223
Banning Space and Motion: The Discretization Program That Shaped Modern Mathematics
Points and the Continuump. 259
Continuity for Numbers: The Triumph of Dedekind's Metaphorsp. 292
Calculus Without Space or Motion: Weierstrass's Metaphorical Masterpiecep. 306
Le trou normand: A Classic Paradox of Infinityp. 325
Implications for the Philosophy of Mathematics
The Theory of Embodied Mathematicsp. 337
The Philosophy of Embodied Mathematicsp. 364
e[superscript pi i] + 1 = 0 A Case Study of the Cognitive Structure of Classical Mathematics
Analytic Geometry and Trigonometryp. 383
What Is e?p. 399
What Is i?p. 420
e[superscript pi i] + 1 = 0--How the Fundamental Ideas of Classical Mathematics Fit Togetherp. 433
Referencesp. 453
Indexp. 473
Table of Contents provided by Syndetics. All Rights Reserved.

ISBN: 9780465037711
ISBN-10: 0465037712
Audience: Professional
Format: Paperback
Language: English
Number Of Pages: 512
Published: 16th August 2001
Country of Publication: US
Dimensions (cm): 23.6 x 19.1  x 2.6
Weight (kg): 0.9
Edition Number: 1